Bottom Line:
The simulations were realised using the computational fluid dynamic (CFD) software CFD ACE+.The sensitivity of the focused capacitor geometry was evaluated to be S(i) = 0.3 fC/nL.The simulation results are validated by experiments which exhibit good agreement.

ABSTRACTIn this paper a multi-disciplinary simulation of a capacitive droplet sensor based on an open plate capacitor as transducing element is presented. The numerical simulations are based on the finite volume method (FVM), including calculations of an electric field which changes according to the presence of a liquid droplet. The volume of fluid (VOF) method is applied for the simulation of the ejection process of a liquid droplet out of a dispenser nozzle. The simulations were realised using the computational fluid dynamic (CFD) software CFD ACE+. The investigated capacitive sensing principle enables to determine the volume of a micro droplet passing the sensor capacitor due to the induced change in capacity. It could be found that single droplets in the considered volume range of 5 nL < V(drop) < 100 nL lead to a linear change of the capacity up to ΔQ < 30 fC. The sensitivity of the focused capacitor geometry was evaluated to be S(i) = 0.3 fC/nL. The simulation results are validated by experiments which exhibit good agreement.

f6-sensors-12-10550: Change in charge as a function of time caused by spherically shaped droplets of different volumes passing the capacitor as shown in the illustration for a spherical droplet of V = 50 nL at three specific points in time.

Mentions:
To investigate the feasibility to solve the described multi-disciplinary problem the presented computational model was used in a simplified setup. Simulations were performed with defined spherical droplets of various volumes in the range from 5 to 100 nL neglecting the described droplet generation model. The droplets were defined as initial conditions in the model passing the capacitor with a constant shape at a defined velocity of v = 1 m/s. The charge characteristic on the measurement electrode was extracted as a function of time and is given in Figure 6 for five individual droplet sizes. The almost symmetric signals reflect the flight of the spherical droplets through the capacitor. The maximum change in charge is reached when the droplet approaches the horizontal centreline of the capacitor, like shown in Figure 6 (Δt = 2.6 ms at V = 50 nL). Like expected, the maximum charge alternation increases with higher droplet volumes, thus the feasibility to apply the sensor for volume measurements is confirmed. However, these simulations do not reflect the known signal characteristics, in particular the non-symmetric signal shape including the negative dip gained from experiments as displayed in Figure 1. Therefore, the full model of the dispensing process has to be considered to include the droplet tear off process as well as the effect of capacitive coupling.

f6-sensors-12-10550: Change in charge as a function of time caused by spherically shaped droplets of different volumes passing the capacitor as shown in the illustration for a spherical droplet of V = 50 nL at three specific points in time.

Mentions:
To investigate the feasibility to solve the described multi-disciplinary problem the presented computational model was used in a simplified setup. Simulations were performed with defined spherical droplets of various volumes in the range from 5 to 100 nL neglecting the described droplet generation model. The droplets were defined as initial conditions in the model passing the capacitor with a constant shape at a defined velocity of v = 1 m/s. The charge characteristic on the measurement electrode was extracted as a function of time and is given in Figure 6 for five individual droplet sizes. The almost symmetric signals reflect the flight of the spherical droplets through the capacitor. The maximum change in charge is reached when the droplet approaches the horizontal centreline of the capacitor, like shown in Figure 6 (Δt = 2.6 ms at V = 50 nL). Like expected, the maximum charge alternation increases with higher droplet volumes, thus the feasibility to apply the sensor for volume measurements is confirmed. However, these simulations do not reflect the known signal characteristics, in particular the non-symmetric signal shape including the negative dip gained from experiments as displayed in Figure 1. Therefore, the full model of the dispensing process has to be considered to include the droplet tear off process as well as the effect of capacitive coupling.

Bottom Line:
The simulations were realised using the computational fluid dynamic (CFD) software CFD ACE+.The sensitivity of the focused capacitor geometry was evaluated to be S(i) = 0.3 fC/nL.The simulation results are validated by experiments which exhibit good agreement.

ABSTRACTIn this paper a multi-disciplinary simulation of a capacitive droplet sensor based on an open plate capacitor as transducing element is presented. The numerical simulations are based on the finite volume method (FVM), including calculations of an electric field which changes according to the presence of a liquid droplet. The volume of fluid (VOF) method is applied for the simulation of the ejection process of a liquid droplet out of a dispenser nozzle. The simulations were realised using the computational fluid dynamic (CFD) software CFD ACE+. The investigated capacitive sensing principle enables to determine the volume of a micro droplet passing the sensor capacitor due to the induced change in capacity. It could be found that single droplets in the considered volume range of 5 nL < V(drop) < 100 nL lead to a linear change of the capacity up to ΔQ < 30 fC. The sensitivity of the focused capacitor geometry was evaluated to be S(i) = 0.3 fC/nL. The simulation results are validated by experiments which exhibit good agreement.